Plug-and-Play Methods for Magnetic Resonance Imaging: Using Denoisers for Image Recovery

Magnetic resonance imaging (MRI) is a noninvasive diagnostic tool that provides excellent soft-tissue contrast without the use of ionizing radiation. Compared to other clinical imaging modalities (e.g., computed tomography or ultrasound), however, the data acquisition process for MRI is inherently slow, which motivates undersampling; thus, there is a need for accurate, efficient reconstruction methods from undersampled data sets. In this article, we describe the use of plug-and-play (PnP) algorithms for MRI image recovery. We first describe the linearly approximated inverse problem encountered in MRI. Then, we review several PnP methods for which the unifying commonality is to iteratively call a denoising subroutine as one step of a larger optimization-inspired algorithm. Next, we describe how the result of the PnP method can be interpreted as a solution to an equilibrium equation, allowing convergence analysis from this perspective. Finally, we present illustrative examples of PnP methods applied to MRI image recovery.